Update 2005

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Update 2005
Deutsches Forschungszentrum für Künstliche
Intelligenz
Erica Melis

• German Research Center for Artificial
  Intelligence (DFKI)
• Universität des Saarlandes
• Saarbrücken, Germany

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ActiveMath Learning Environment

• Web-based
• Adaptive course generation
• Adaptive presentation
• Semantic knowledge representation
• Learner model
• Pedagogical knowledge
• Interactive exercises
• Suggestion mechanism
• Semantic XML-representation
• Web-presentation of maths

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Hauptmenu
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Multi-Lingual Chinese
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Evas Books
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Different users same topic

• Anton
• Mathematics
• Bachelor student
• Group theory
• Exam exercises
• Train interactively
• At home

• Eva
• Computer science
• PhD student
• Group theory
• Profound knowledge
• Overview
• At university

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A Book
Good mastery
Medium mastery
Weak mastery
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A Book
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Scenario Overview
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Scenario Exam
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Adaptive Course Generation
MBase OMDoc
Pedagogical Rules
Course Generator
User Model
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Example Course Generation

• CG Automatic assembly of learning objects taking
  into account learner properties
• Operator ProvideAdequateExerciseFor(C)
• if mastery(C)lt0.3 then Exercise(easy),
• if 0.3mastery(C)lt0.7 then Exercise(medium),
• if 0.7mastery(C)lt1 then Exercise(hard).
• Ontology provides vocabulary at the adequate
  level of abstraction for defining complex domain
  independent pedagogical strategies
• moderate constructivist strategies
• traditional didactic strategies

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Knowledge Representation

• Metadata
• Mathematical dependencies for, theory
• Pedagogical dependencies prerequisites, against
• Pedagogical characteristics difficulty,
  competencies..
• OMDoc / OpenMath
• Structures theory, definition, axiom, example
• Mathematical semantics

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OMDoc definition of a monoid
ltdefinition id"c6s1p4_Th2_def_monoid"
for"c6s1p4_monoid ltmetadatagt ltdepends-ongt
ltref theory"cp1_Th3" name"structure" /gt
lt/depends-ongt ltTitle xmllang"en"gtDefinition
of a monoidlt/Titlegt lt/metadatagt ltCMP
xmllang"en" format"omtext"gt A monoid is a
ltref xref"cp1_Th3_def_structure"gt structure
lt/refgt ltOMOBJgt ltOMS cd"elementary"
name"ordered-triple"/gt ltOMV name"M"/gt
ltOMS cd"cp4_Th2" name"times"/gt ltOMS
cd"cp4_Th2" name"unit"/gt lt/OMOBJgt in
which ltOMOBJgt ltOMS cd"elementary"
name"ordered-pair"/gt ltOMV name"M"/gt ltOMS
cd"cp4_Th2" name"times"/gt lt/OMOBJgt is a
semi-group with ltref xref"c6s1p3_Th2_def_unit"gtelt
/refgt ltOMOBJ xmlns"http//www.openmath.org/O
penMath"gt ltOMS cd"cp4_Th2" name"unit"/gt
lt/OMOBJgt. lt/CMPgt ltFMPgtltOMOBJgt ...
lt/OMOBJgtlt/FMPgt lt/definitiongt
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OMDoc ontology

• Content items
• unique ID

Concept
Satellite
Definition
Assertion
Example
Elaboration
Proof
Axiom
Exercise
summary
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OpenMath usage

• invisible presentation of semantics
• copy and paste of formulae
• from content
• to formula-input
• to external services
• search formulae
• with reformulation
• with fuzziness

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Essentials for true Usability

• Implement what learners need
• Test and evaluate in realistic environments
• 70 students, 4 months in Gesamtschule Bellevue
• 40 students, 2 weeks Augsburg
• 50 at Edinburgh and Malaga
• 250 students at Westminster University London
• Clean engineering, architecture
• Scalability
• ready-to-use, stable
• Adaptive hypermedia, semantic Web representation,
  ontologies, planning, domain reasoning,
  diagnosis, ML, user modeling

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Web-Service Architecture

• for integration of components and tools from
  several partners (interoperability and reuse)
• protocols
• interfaces
• Configurable open system
• Scalability
• Usage of existing components

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MVC Architecture
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Event Framework

• Components can publish and subscribe
• Event object Type, timestamp, source,
• Asynchronous messaging between components
• Used for
• Generic component integration
• User logging
• User modeling
• better scalability clients can poll events

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Example Course Generation
Event BookAdded
Event tutorialRequest-Planned
Content Structure
Queries about Content
User request (http request) tutorialRequest
Queries about Learner
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Presentation Naive Approach to Delivery

• Naive approach
• Start with table of contents
• Bring XML-fragments together
• Apply XSLT transformation
• Issues
• Low performance
• Adaptivity logic defined in XSLT
• Layout defined in XSLT

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Presentation Component

• Idea 2-stage approach for presentation
• First stage deals with individual content
  fragments
• Second stage combines fragments to user-specific
  pages, enriched with dynamic data

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Specifically Presentation of Mathematics

• Mathematics on the Web is a problem
• Often only as images
• No semantics
• ActiveMath
• HTML, MathML, (SVG)
• Cross-browser Internet Explorer, Mozilla
• Usage of semantics to add invisible information
• Authorable appearance

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Advantages of the Presentation System

• Multi-formats
• HTML, XHTMLMathML, PDF, SVG, slides
• Caching real performance much higher
• Incremental rendering
• High flexibility
• Separation of concerns (MVC)
• Easier layout changes
• can use semantic information

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Math HMTL
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Math XHTMLMathML
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Math PDF

• SVG

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Maths. Semantics rendered
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Specific Notation Presentationcountry,
author-specific
ltnotation format"htmlpmathmlTeX"
precedence"1000"gt lt?OMPE linearm_f,P
qmathacsl(f,P) ?gt ltmathgt ltmsubgt
ltmogtmlt/mogt ltmrowgt
ltmi amprecedence"1000"gtflt/migt
ltmogt,lt/mogt ltmi amprecedence"1000"gtPlt
/migt lt/mrowgt lt/msubgt
lt/mathgt ltOMOBJgt ltOMAgt
ltOMS cd"deriv_symbols" name"slope"/gt
ltOMV name"f"/gt ltOMV name"P"/gt
lt/OMAgt lt/OMOBJgt lt/notationgt
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Exercise Subsystem
Queries to (mathematical) Services

• Services CASs, domain reasoners
• recursive queries
• Format (name, maths objects, context, depth)
• (getResult, semEquivObject, C, inf)
• (getResult, syntEquivObject, 0, inf)
• (getRelevance, (t, input), C, inf)
• getNextResult (getResult, t,C, 1)
• (getUserSolutionPath, (t,input), C, n)
• (getConcept, t, C, n)